Questions: Multiply (3+2i)(3-2i)

Multiply (3+2i)(3-2i)
Transcript text: Multiply \[ (3+2 i)(3-2 i) \]
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Solution

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Solution Steps

Step 1: Multiplication

To multiply two complex numbers, we use the distributive property: \((a + bi)(c + di)\).

Step 2: Expansion

Applying the distributive law gives us: \(ac + adi + bci + bdi^2\).

Step 3: Simplification

Remembering that \(i^2 = -1\), we simplify the expression to: \(ac + adi + bci - bd\).

Step 4: Combine Like Terms

Combining the real parts and the imaginary parts, we get: \((ac - bd) + (ad + bc)i\).

Final Answer:

The simplified product of the two complex numbers is: \(13 + 0i\).

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